For small angle, sin^2(alpha) ~= (alpha^2). So a place to look might be when alpha = 1/2

My calculator converges on .5545

Then, there's probably something wrong with your calculator. :tongue2:
You can always put x back to the original equation, and find out that it is not a solution... :tongue:
By the way, the problem reads:
[tex]\sin ^ 2 \alpha = \frac{\alpha}{2}[/tex].